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* to you under the Apache License, Version 2.0 (the
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*
* http://www.apache.org/licenses/LICENSE-2.0
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* Unless required by applicable law or agreed to in writing,
* software distributed under the License is distributed on an
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*/
package org.apache.datasketches.theta;
import static java.lang.Math.max;
import static java.lang.Math.min;
import static org.apache.datasketches.BoundsOnRatiosInThetaSketchedSets.getEstimateOfBoverA;
import static org.apache.datasketches.BoundsOnRatiosInThetaSketchedSets.getLowerBoundForBoverA;
import static org.apache.datasketches.BoundsOnRatiosInThetaSketchedSets.getUpperBoundForBoverA;
import static org.apache.datasketches.Util.MAX_LG_NOM_LONGS;
import static org.apache.datasketches.Util.MIN_LG_NOM_LONGS;
import static org.apache.datasketches.Util.ceilingPowerOf2;
/**
* Jaccard similarity of two Theta Sketches.
*
* @author Lee Rhodes
*/
public final class JaccardSimilarity {
private static final double[] ZEROS = {0.0, 0.0, 0.0}; // LB, Estimate, UB
private static final double[] ONES = {1.0, 1.0, 1.0};
/**
* Computes the Jaccard similarity ratio with upper and lower bounds. The Jaccard similarity ratio
* J(A,B) = (A ^ B)/(A U B) is used to measure how similar the two sketches are to each
* other. If J = 1.0, the sketches are considered equal. If J = 0, the two sketches are
* distinct from each other. A Jaccard of .95 means the overlap between the two
* populations is 95% of the union of the two populations.
*
* Note: For very large pairs of sketches, where the configured nominal entries of the sketches
* are 2^25 or 2^26, this method may produce unpredictable results.
*
* @param sketchA given sketch A
* @param sketchB given sketch B
* @return a double array {LowerBound, Estimate, UpperBound} of the Jaccard ratio.
* The Upper and Lower bounds are for a confidence interval of 95.4% or +/- 2 standard deviations.
*/
public static double[] jaccard(final Sketch sketchA, final Sketch sketchB) {
//Corner case checks
if ((sketchA == null) || (sketchB == null)) { return ZEROS.clone(); }
if (sketchA == sketchB) { return ONES.clone(); }
if (sketchA.isEmpty() && sketchB.isEmpty()) { return ONES.clone(); }
if (sketchA.isEmpty() || sketchB.isEmpty()) { return ZEROS.clone(); }
final int countA = sketchA.getRetainedEntries();
final int countB = sketchB.getRetainedEntries();
//Create the Union
final int minK = 1 << MIN_LG_NOM_LONGS;
final int maxK = 1 << MAX_LG_NOM_LONGS;
final int newK = max(min(ceilingPowerOf2(countA + countB), maxK), minK);
final Union union =
SetOperation.builder().setNominalEntries(newK).buildUnion();
union.update(sketchA);
union.update(sketchB);
final Sketch unionAB = union.getResult();
final long thetaLongUAB = unionAB.getThetaLong();
final long thetaLongA = sketchA.getThetaLong();
final long thetaLongB = sketchB.getThetaLong();
final int countUAB = unionAB.getRetainedEntries();
//Check for identical data
if ((countUAB == countA) && (countUAB == countB)
&& (thetaLongUAB == thetaLongA) && (thetaLongUAB == thetaLongB)) {
return ONES.clone();
}
//Create the Intersection
final Intersection inter = SetOperation.builder().buildIntersection();
inter.update(sketchA);
inter.update(sketchB);
inter.update(unionAB); //ensures that intersection is a subset of the union
final Sketch interABU = inter.getResult(true, null);
final double lb = getLowerBoundForBoverA(unionAB, interABU);
final double est = getEstimateOfBoverA(unionAB, interABU);
final double ub = getUpperBoundForBoverA(unionAB, interABU);
return new double[] {lb, est, ub};
}
/**
* Returns true if the two given sketches have exactly the same hash values and the same
* theta values. Thus, they are equivalent.
* @param sketchA the given sketch A
* @param sketchB the given sketch B
* @return true if the two given sketches have exactly the same hash values and the same
* theta values.
*/
public static boolean exactlyEqual(final Sketch sketchA, final Sketch sketchB) {
//Corner case checks
if ((sketchA == null) || (sketchB == null)) { return false; }
if (sketchA == sketchB) { return true; }
if (sketchA.isEmpty() && sketchB.isEmpty()) { return true; }
if (sketchA.isEmpty() || sketchB.isEmpty()) { return false; }
final int countA = sketchA.getRetainedEntries();
final int countB = sketchB.getRetainedEntries();
//Create the Union
final Union union =
SetOperation.builder().setNominalEntries(ceilingPowerOf2(countA + countB)).buildUnion();
union.update(sketchA);
union.update(sketchB);
final Sketch unionAB = union.getResult();
final long thetaLongUAB = unionAB.getThetaLong();
final long thetaLongA = sketchA.getThetaLong();
final long thetaLongB = sketchB.getThetaLong();
final int countUAB = unionAB.getRetainedEntries();
//Check for identical counts and thetas
if ((countUAB == countA) && (countUAB == countB)
&& (thetaLongUAB == thetaLongA) && (thetaLongUAB == thetaLongB)) {
return true;
}
return false;
}
/**
* Tests similarity of a measured Sketch against an expected Sketch.
* Computes the lower bound of the Jaccard ratio JLB of the measured and
* expected sketches.
* if JLB ≥ threshold, then the sketches are considered to be
* similar with a confidence of 97.7%.
*
* @param measured the sketch to be tested
* @param expected the reference sketch that is considered to be correct.
* @param threshold a real value between zero and one.
* @return if true, the similarity of the two sketches is greater than the given threshold
* with at least 97.7% confidence.
*/
public static boolean similarityTest(final Sketch measured, final Sketch expected,
final double threshold) {
//index 0: the lower bound
//index 1: the mean estimate
//index 2: the upper bound
final double jRatioLB = jaccard(measured, expected)[0]; //choosing the lower bound
return jRatioLB >= threshold;
}
/**
* Tests dissimilarity of a measured Sketch against an expected Sketch.
* Computes the upper bound of the Jaccard ratio JLB of the measured and
* expected sketches.
* if JUB ≤ threshold, then the sketches are considered to be
* dissimilar with a confidence of 97.7%.
*
* @param measured the sketch to be tested
* @param expected the reference sketch that is considered to be correct.
* @param threshold a real value between zero and one.
* @return if true, the dissimilarity of the two sketches is greater than the given threshold
* with at least 97.7% confidence.
*/
public static boolean dissimilarityTest(final Sketch measured, final Sketch expected,
final double threshold) {
//index 0: the lower bound
//index 1: the mean estimate
//index 2: the upper bound
final double jRatioUB = jaccard(measured, expected)[2]; //choosing the upper bound
return jRatioUB <= threshold;
}
}